Triangle Review 05:09 minutes

Video Transcript

Transcript Triangle Review

Sherlock Bones is on a new case… Old Lady Miller was mugged, and a very precious item was stolen! It all happened so fast... she doesn’t remember much, but she does remember the image of a polygon with three sides and three angles. Bones, the super sleuth, knows right away that the shape she describes is a triangle, and the interior angles sum to 180-degrees. But that's not enough information to solve the crime, so…

Categorizing Triangles

Sherlock Bones hypnotizes Old Lady Miller and uncovers three more very important details: First, the triangle shape has no angles larger than 90°. From this, Bones concludes the wanted triangle cannot be obtuse because an obtuse triangle contains an angle that's greater than 90°. Second, there's one 90° angle, so Bones knows the triangle has to be a right triangle. The last detail: exactly two sides of the triangle have the same length, so he knows it must be an isoceles triangle, not an equilateral. Will these clues help him find the mugger? I sure hope so!
Bones tries to recall all the different types of triangles, but the situation is getting out of control. Let's help Bones organize the characteristics of these three-cornered shapes. Triangles can be categorized by their angles or their side lengths. Obtuse triangles have one angle greater than 90°. Acute triangles have all angles less than 90°, equilateral triangles have all angles measuring 60° and right triangles have exactly one 90° angle.
Categorizing triangles by their side lengths is just two sides of the same coin. In a triangle, the bigger the angle measure, the longer the side length. None of the sides of a scalene triangle are the same. Isosceles triangles have at least two sides that are the same length while all sides of an equilateral triangle are the same. This means that some triangles may fit into more than one category. This is not the news Bones wants to hear. Bones has a list of five suspects that may fit the description. Can he identify the thief with these clues?

Analyzing different Triangles

He uses the process of elimination to rule out the suspects one by one. The first suspect has a triangle shape on his tie: One angle has a measurement of 110° – this is clearly larger than 90°, making this an obtuse triangle. Before Bones releases this suspect, he double checks the shape with the clues. The triangle cannot contain a 90° angle because if one angle is greater than 90°, the sum of all three angles will be greater than 180°. Also, although two sides of the triangle have the same length, the triangle is an isosceles triangle but not equilateral triangle which has three equal sides. Bones releases this suspect.
The second suspect in the line-up has a triangle-shaped goatee. His facial fuzz is the same length on all three sides, so all three angles are equal to 60°, and the triangle is acute - not an obtuse or right. Plus, not only is the triangle an isosceles triangle, but it's also an equilateral triangle. Sherlock lets this suspect walk.
The third suspect has a triangle pendant on her necklace. The pendant has an angle measuring 50°. Since the angle is less than 90°, the shape is an acute triangle, not a right or an obtuse triangle. Since the other two angles are the same, they measure 65°, the two corresponding sides must have the same length. The triangle pendant is in the shape of an isosceles triangle - not an equilateral, so this suspect is not the guilty party.
The fourth suspect sports a triangle hair...band...thing. The side lengths of the shape are all different, so it's a scalene triangle, not an isosceles triangle. This woman isn't a thief. She gets to fly the coop, too. The last suspect has a triangle handkerchief in his jacket pocket. Bones knows that two of the angles measure 45°, so the missing angle is 90°, this shape is definitely a right triangle – not obtuse. So far, so good. Because the two angles are equal, the two corresponding sides have the same length, so this shape is an isosceles triangle – not an equilateral.

It's incredible! Bones has the evidence to prove the crime, so the thief will have to do the time! Are you wondering what the thief stole from the old lady? He stole her heart.